Robert Gilmer's Faculty Page

Robert Gilmer
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Emertius Professor
Ph.D., Louisiana State University, USA

Detailed description of research

Zero-dimensional Commutative Rings
There have been significant advances in the theory of zero-dimensional commutative rings in the last decade, but there remain topics within the area where there are wide gaps in the theory. Two of these topics in which I am interested are the topic of realizability of a family of fields as the family of residue fields of a zero-dimensional ring, and the topic of embeddability of a commutative ring in a zero-dimensional ring. Related to the second topic there are a number of questions concerning decomposition of ideals as an infinite intersection of primary ideals that are of independent interest.

Rings of Integer-Valued Polynomials
Again this this an area in which much work has been done during the last twenty years. My primary interest here is in the problem of identifying and/or characterizing elements in a ring of integer-valued polynomials that are strong 2-generators---that is, which have the property that they serve as one of two generators of each finitely generated ideal to which they belong. This question is of interest when the base ring under consideration consists of algebraic integers, and has not been completely resolved even in the case of the classical ring of integer-valued polynomials on the ring Z of rational integers.